Daily Wheeler and Hendon MJO Index, which can be accessed here:
http://www.cawcr.gov.au/bmrc/clfor/cfstaff/matw/maproom/RMM/

MJO CLASSIFICATION:

The Wheeler-Hendon MJO index (RMM1 and RMM2) includes (1) phase information -- there are eight phases and they show where the MJO wave is convectively active, and (2) amplitude information -- when there is a strong projection on the MJO the amplitude is greater than one. Classification of an MJO event depends on three major requirements. First, the MJO index must have amplitude greater than one for consecutive pentads. Second, the MJO index must include phases that are in numerical order (i.e. phases 2, 3, 5, 6, 8, 1, 2). Third, MJO events must last longer than five pentads (25 days) and cannot remain stationary in one phase for more than four pentads (20 days).

Note that there are instances where some more subjective examinations are required. For example, if there is a clear MJO event with substantial duration then we will still include it even though one pentad dips slightly below an amplitude of one. Or possibly the phase will become non-consecutive for one day (i.e. phases 2, 3, 2, 4). We will still include these isolated instances if they are infrequent and part of a larger MJO event.

DEFINITION OF TERMS:

“Raw anomalies”refers to the daily temperature anomalies that are obtained by removing 30-year daily climatology (1979-2008), so that the annual cycle is removed.

“Filtered anomalies” refers to the 20-100 band-pass filter (Murakami, 1979) that is applied to the daily “raw anomalies” with the peak period of 45 days. Note that the “filtered anomalies” are calculated to best isolate intra-seasonal, MJO timescales (i.e. excludes the decadal trend).

DESCRIPTION OF IMAGES:

Eight composites are created from the eight Wheeler Hendon MJO phases (numbered 1-8), which are associated with an enhanced convective signal in a certain longitude region of the tropics. For example, Phases 2 and 3 describe enhanced convection across the equatorial Indian Ocean and suppressed convection over the Maritime Continent and western equatorial Pacific Ocean (Wheeler and Hendon, 2004). Phases 7 and 8 indicate enhanced convection across the tropical western and central Pacific Ocean and suppressed convection over the eastern Indian Ocean and Maritime Continent.

(a) “Composites/Significance” Section (unmasked composites)

Left 8 panels: For each 3month season, 8 MJO phases are displayed showing the “raw anomalies” composites that are unmasked. The anomalies shown are not necessarily statistically significant or associated with MJO even though they are averaged according to the eight MJO phases.

Right 8 panels: Displayed as in the left panel except showing the level of statistical significance. Purple/blue shaded areas (lower percentages) represent regions that have higher levels of statistical significance according to a Monte Carlo test (see details in methodology). In these plots, a significance level of 5% means that there is a 5% chance that the anomalies arise from random chance (also known as the 95% confidence level).

For each 3month season, the masked composited anomalies for each of the 8 MJO phases are displayed.

The 0% section shows shading where anomalies are at least at the 5% level of significance (using Monte Carlo).

The 60% and 70% sections show anomalies that are at least at the 5% level of significance and when only the days that show agreement between the “raw” anomalies and the “filtered anomalies” (see methodology for more detail). As a rule of thumb, the higher the percentage, the more certainty exists indicating the “raw anomalies” composite is due to intra-seasonal, MJO variability. 60% means that 60% of days show agreement between “raw anomalies” and “filtered anomalies” at each grid point.

METHODOLOGY:

For each 3-month overlapping season:

Assessing significance:
Significance of these “raw anomalies” composites are tested with a Monte Carlo test:

(a) A large number (800) of randomly generated composites are created for each season. The composites are created from randomly sampling the entire historical record (with replacement). The number of degrees of freedom remains consistent between the observed MJO composites and the randomly generated composites (for example, if there are 7 consecutive days in Phase 8 in the MJO composite than the random sampling will extract 7 consecutive days somewhere in the full record).

(b) Significance maps are created by calculating the percent (%) of times the anomaly in the observed MJO composite is exceeded by the anomalies in the 800 randomly generated composites.

Matching with intraseasonal timescales (creating the 60% and 70% masks):
For MJO days, the remaining, unfiltered “raw anomalies” are then tested for agreement with the “filtered anomalies.” Agreement between the two temperature datasets gives more confidence that the response is a result of intra-seasonal, MJO variability. Disagreement between the two datasets suggests that the “raw anomalies” may be capturing variability that is unrelated to MJO timescales. The procedure is as follows:

(a) At each grid point, the “raw” and “filtered” data temperature time series are normalized by their standard deviations. Any day greater than 1 standard deviation is “above-average” and any day below -1 standard deviations is considered “below-average.”

(b) At each grid point, a ratio is calculated for the number of days when both the “raw anomalies” and the “filtered anomalies” are in agreement (i.e. both above-average or both below-average). For above-average and below-average days, this ratio is calculated as:
(# days in agreement in both “raw” and “filtered” data) / (# days in “raw anomalies”)

Example: At one grid point, there are 100 above-average days in the “raw anomalies.” However, those 100 above-average days are only matched by above-average days in the corresponding “filtered anomalies” for 60 of those days, while the rest 40 days are average or below average. Therefore, at that one grid point, 60% of the days are in agreement while 40% of those days are in disagreement.

(c) The percentage of agreement is then used as a mask for the “raw anomalies” composites (along with the 95% confidence level).
Contact: Shuntai.Zhou@noaa.gov if you have any questions or comments.